求解准确的表面张力-重力波方程的新方法

A Novel Method of Solving the Exact Equations for Capillary-Gravity Waves

本文提供一个求解重力和表面张力同时作用的周期前进二维非线性波的新方法.自由表面在计算域转入单位圆后用有限项Fourier级数表示.动力学边界条件用的是完整的非线性形式.Fourier级数的系数用Newton-Raphson方法迭代求解.这是一个精巧的方法.所用计算工作量小而结果精度高.

A new method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The nonlinear surface is expressed by Fourier series with finite number of terms, after the computational domain is transformed into a unit circle. The dynamic boundary equation is used in its exact nonlinear form and the coefficients of Fourier series are found by the Newton-Raphson method successively. This is a neat method, yielding high precision with little computational effort.